Unified Geometric Lattice Theory (UGLT): Deriving Gauge Couplings, Mass Spectra, and Gravity from a K = 12 Vacuum

The Standard Model of particle physics and General Relativity stand as the two pillars of modern physics, yet they remain mathematically incompatible and rely on approximately 19 arbitrary parameters. We present Unified Geometric Lattice Theory (UGLT), a discrete formulation of quantum gravity that derives these parameters from the geometry of a Face-Centered Cubic (FCC) vacuum lattice (K = 12). By identifying the gauge fields with the link variables of the Cuboctahedron unit cell, we demonstrate that the Standard Model gauge group GSM ⊂SU(4) emerges via geometric symmetry breaking. We analyti- cally derive the weak mixing angle sin2 θW = 3/13 by calculating the geometric flux capacity of the lattice sectors, interpreting the angle as a ratio of coupling constants g′2/(g2 +g′2). We further predict a resolution to the Hubble Tension, deriving a local value of H0 = 73.30±0.45 km/s/Mpc from holographic scaling arguments (matching SH0ES data). Finally, we derive General Relativity as the continuum limit of the lattice stress-energy relation. These results suggest that the ”arbitrary” parameters of physics are fixed geometric invariants of a discrete vacuum